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An Adaptive SVD Method for Solving the Pass-Region Problem in S-Transform Time-Frequency Filters

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Chinese Journal of Electronics 2015年第1期24卷 115-123页

作者： YIN Baiqiang HE Yigang LI Bing ZUO Lei YUAN Lifen School of Electrical and Automation Engineering Hefei University of Technology

S-transform(ST) is an excellent tool for time-frequency filter. There are two factors that influence filtering performance: Inverse s-transform(IST) algorithms and the pass-regions in time-frequency domain. A novel matrix IST algorithm is derived and an adaptive singular value decomposition.SVD) method for solving the pass-region problem is proposed. The former can avoid reconstructing errors in time-frequency filtering; the latter is effective to distinguish the pass-region of signal from *** can be realized by removing the smaller singular values and keeping the larger singular values. An additive noise perturbation model is built in ST time-frequency domain and the effective rank of noise perturbation model based on matrix IST is analyzed. Simulation results indicate that the proposed SVD method can provide higher precision than the existing ones at low signal-to-noise ratio and does not need to compute the noise statistics *** examples verify the effectiveness of proposed method.

关键词： S-transform Matrix inverse S-transform Time frequency filter singular value decomposition.

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矩阵方程XT AX=B的一类反问题

高等学校计算数学学报 2004年第3期26卷 222-229页

作者：郭翠平,胡锡炎,张磊中国地质大学信息工程学院湖南大学数学与计量经济学院湖南省计算中心北京 100083 长沙 410082 长沙 410012

1引言本文用Rn×m表示所有n×m实矩阵全体;SR0n×n表示所有n阶实对称半正定矩阵全体;In表示n阶单位矩阵;A-,A+分别表示矩阵A的一个广义逆和Moore-Penrose广义逆;A≥0表示A为对称半正定矩阵;Sn=(en,en-1,…,e1)∈Rn×n,其中ei为单位阵I... 详细信息

1引言本文用Rn×m表示所有n×m实矩阵全体;SR0n×n表示所有n阶实对称半正定矩阵全体;In表示n阶单位矩阵;A-,A+分别表示矩阵A的一个广义逆和Moore-Penrose广义逆;A≥0表示A为对称半正定矩阵;Sn=(en,en-1,…,e1)∈Rn×n,其中ei为单位阵In的第i列; [n/2]表示不超过n/2的最大整数.

关键词： symmetric matrix bisvmmetric positive semi-definite matrix matrix equation singular value decomposition.

Principal Manifolds and Nonlinear Dimensionality Reduction via Tangent Space Alignment

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Journal of Shanghai University(English Edition) 2004年第4期8卷 406-424页

作者：张振跃查宏远 Department of Mathematics Zhejiang University Yuquan Campus Hangzhou 310027 P.R. China Department of Computer Science and Engineering The Pennsylvania State University University Park PA 16802

We present a new algorithm for manifold learning and nonlinear dimensionality reduction. Based on a set of unorganized data points sampled with noise from a parameterized manifold, the local geometry of the manifold is learned by constructing an approximation for the tangent space at each point, and those tangent spaces are then aligned to give the global coordinates of the data points with respect to the underlying manifold. We also present an error analysis of our algorithm showing that reconstruction errors can be quite small in some cases. We illustrate our algorithm using curves and surfaces both in 2D/3D Euclidean spaces and higher dimensional Euclidean spaces. We also address several theoretical and algorithmic issues for further research and improvements.

关键词： nonlinear dimensionality reduction principal manifold tangent space subspace alignment singular value decomposition.

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SELF-VALIDATING PASSIVE WIRELESS SAW SENSOR

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SELF-VALIDATING PASSIVE WIRELESS SAW SENSOR